Effect of surface parameter on interband surface mode frequencies of finite diatomic chain

Abstract

The surface modes of a finite diatomic chain of alternating atoms ( M 1≠ M 2) are investigated. The surface force constants are assumed to differ from the bulk ones, with the resulting surface parameter a identical on both ends of the chain. The criteria governing the existence of interband surface (IBS) modes with frequencies lying in the forbidden gap between acoustical and optical bulk bands for natural ( a=1) as well as non-natural ( a≠1) surface defects are analyzed by the difference equation method. It is found that the IBS modes localize, depending on the value of the surface parameter a, either at the surface of lighter atoms (if a is positive), or at that of heavier atoms (if a is negative). Two, one or no IBS mode is found to exist in the chain depending on the relation between the mass ratio and surface parameter—the quantities on which the surface localization increment t depends. If two modes (one acoustical and the other optical) are present, their frequencies are displaced symmetrically with respect to the middle of the forbidden gap if the surface defect is natural, and asymmetrically if it is other than natural. If the localization of the IBS mode exceeds a well-defined critical value t c, the mode frequency becomes complex, indicating that the mode undergoes a damping. A comparison of the present results and those obtained by Wallis for the diatomic chain with natural surface defect is also given.